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A174964 Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^2+1 for j = k, M_n(j,k) = n for abs(j-k) = 1, M_n(j,k) = 0 otherwise.

%I A174964 #15 Sep 08 2022 08:45:51
%S A174964 2,21,820,69905,10172526,2238976117,692352720200,285942833483841,
%T A174964 151970818238211610,101010101010101010101,82081105631730092455932,
%U A174964 80052769211806164721787281,92279361920609501281366280390
%N A174964 Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^2+1 for j = k, M_n(j,k) = n for abs(j-k) = 1, M_n(j,k) = 0 otherwise.
%D A174964 J.-M. Monier, Algèbre et géometrie, exercices corrigés. Dunod, 1997, p. 27.
%H A174964 Vincenzo Librandi, <a href="/A174964/b174964.txt">Table of n, a(n) for n = 1..80</a>
%F A174964 a(1) = 2, a(n) = (1-n^(2*n+2))/(1-n^2) for n > 1.
%e A174964 a(5) = determinant(M_5) = 10172526 where M_5 is the matrix
%e A174964   [26  5  0  0  0]
%e A174964   [ 5 26  5  0  0]
%e A174964   [ 0  5 26  5  0]
%e A174964   [ 0  0  5 26  5]
%e A174964   [ 0  0  0  5 26]
%p A174964 with(numtheory):for n from 2 to 25 do:x:=(1-n^(2*n+2))/(1-n^2):print(x):od:
%o A174964 (Magma) [ n eq 1 select 2 else (1-n^(2*n+2))/(1-n^2): n in [1..13] ]; // _Klaus Brockhaus_, Apr 15 2010
%o A174964 (Magma) [ Determinant( SymmetricMatrix( &cat[ [k eq j select n^2+1 else k eq j-1 select n else 0: k in [1..j] ]: j in [1..n] ] ) ): n in [1..13] ]; // _Klaus Brockhaus_, Apr 15 2010
%Y A174964 Cf. A174963.
%K A174964 nonn
%O A174964 1,1
%A A174964 _Michel Lagneau_, Apr 02 2010
%E A174964 Edited by _Klaus Brockhaus_, Apr 15 2010